# Thread: Interval estimation of an exponential function

1. ## Interval estimation of an exponential function

Hi, I was trying to solve this question (which is assigned to me) from Stapleton's book (7.7.1.a).

I have a solution which is not correct but I couldn't understand where am I wrong? And couldn't understand the solution of the author.

I hope you can see the following gif image.

2. Originally Posted by bilgedama
Hi, I was trying to solve this question (which is assigned to me) from Stapleton's book (7.7.1.a).

I have a solution which is not correct but I couldn't understand where am I wrong? And couldn't understand the solution of the author.

I hope you can see the following gif image.

All you need to do is find $\displaystyle $$\theta_{0.9} such that: \displaystyle P(X\ge x|\theta_{0.9})<0.1 where \displaystyle$$x$ is the observation, which is the solution for $\displaystyle$$\theta_{0.9}$ to:

$\displaystyle e^{-x/\theta_{0.9}}=0.9$

which is:

$\displaystyle \displaystyle \theta_{0.9}=\frac{x}{\ln(0.9)}$

CB

3. Thank you for the answer. Which step of my solution is not correct?
I suspect my result about the distribution of T/(2lamba) is not correct. ?